In article the algorithm of calculation of systems with unilateral constraints with the replacement reactions of the supports on the force variables. The calculation algorithm is based on the finite element method in the form of the classical mixed method. The algorithm of search of version of the working constructive scheme is based on the modified "physically obvious" algorithm of design constructively nonlinear systems. The paper describes the features of the resolution system of the algorithm proposed by the authors and provides a flowchart. A comparative analysis with the algorithm of calculation of systems with unilateral constraints, proposed by the authors earlier, as well as some others. The efficiency of the algorithm is tested on numerical examples.The advantages of the proposed algorithm are: The vector of results includes the reaction of the support, which allows you to make a decision to change the design scheme; the calculation takes into account, as an additional loading factor, the size of the displasement in the realized one-way support, which increases the accuracy of the calculation.